Constructive role of noise and diffusion in an excitable slow–fast population system

We study the effects of noise and diffusion in an excitable slow-fast population system of the Leslie-Gower type. The phenomenon of noise-induced excitement is investigated in the zone of stable equilibria near the Andronov-Hopf bifurcation with the Canard explosion. The stochastic generation of mixed-mode oscillations is studied by numerical simulation and stochastic sensitivity analysis. Effects of the diffusion are considered for the spatially distributed variant of this slow-fast population model. The phenomenon of the diffusion-induced generation of spatial patterns-attractors in the Turing instability zone is demonstrated. The multistability and variety of transient processes of the pattern formation are discussed. © 2020 The Author(s) Published by the Royal Society. All rights reserved. Russian Science Foundation, RSF: 16-11-10098 Data accessibility. This article does not contain any additional data. Authors’ contributions. All authors contributed equally to this study. Competing interests. We declare we have no competing interests. Funding. The work was supported by Russian Science Foundation (grant no. 16-11-10098).